I made these using *Stella 4d*, a program you can try as a free trial download at http://www.software3d.com/Stella.php.

# Tag Archives: rhombic

# Two Rhombic Polyhedra with Tessellated Faces

These polyhedra are the rhombic dodecahedron (above), and the rhombic triacontahedron (below).

I made both of these using* Stella 4d*, which you can try for free at http://www.software3d.com/Stella.php. The tessellation on the faces of these polyhedra first appeared right here on this blog, in the post just before this one.

# The Golden Rhombus, the Rhombic Triacontahedron, and the Rhombic Hexecontahedron

There’s a special rhombus which is called the “golden rhombus,” because its diagonals are in the golden ratio. To construct it with compass and straight edge, you first construct a golden rectangle (shown with blue edges and a yellow interior), and then connect the midpoints of its sides to form a rhombus (with edges shown in red).

Several polyhedra can be made which use golden rhombi as their faces. The most well-known of these polyhedra is the rhombic triacontahedron, which has 30 such faces. It is the dual of the icosidodecahedron.

If the rhombic triacontahedron is stellated 26 times, the result is the (non-convex) rhombic hexecontahedron. It has 60 golden rhombi as faces.

Both of these polyhedra can be constructed with Zometools (available at http://www.zometool.com). With white Zomeballs and red Zomestruts, these polyhedra look a lot like this:

The flat image at the top of this post was created using *Geometer’s Sketchpad* and *MS-Paint*. The four rotating polyhedral images were created using *Stella 4d: Polyhedron Navigator*, which you can purchase, or try for free, at http://www.software3d.com/Stella.php.

# A Rhombic Dodecahedron, Made of Icosahedra, and Tall Triangular Antiprisms

Software used: *Stella 4d*, available at http://www.software3d.com/Stella.php.

# A Flock of 32 Rhombic Triacontahedra

Software used: *Stella 4d*, available at http://www.software3d.com/Stella.php.

# A Rhombic Cage

This cage is made of 36 identical rhombi, and has six openings. I made it with *Stella 4d*, a program available at this website.

# Partially Truncated Platonic and Rhombic Dodecahedra

Each of these dodecahedra were modified by truncations at exactly four of their three-valent vertices. As a result, each has four equilateral triangles as faces. In the one above, the Platonic dodecahedron’s pentagonal faces are modified into a dozen irregular hexagons by these truncations, while, in the one below, the rhombic dodecahedron’s faces are modified into twelve irregular pentagons.

Both of these polyhedra were created using *Stella 4d*, software you can try for yourself at this website.